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Robots are often used in industry to handle flexible objects, such as frames, leather goods, thin plates and rubber tubes. Most of the earlier studies dealt with handling of rigid objects and only a few have focused on the collaborative manipulators handling flexible objects. Therefore in this book two rigid robot manipulators collaboratively moving the flexible object in the desired trajectory and also suppressing the vibration of the object are considered for the study. The complete system of dynamic equations is obtained with the help of derived kinematic relations and dynamic equations of manipulators as well as the flexible object. Then, by employing singular perturbation technique slow and fast subsystems are identified. In order to handle parameter uncertainties, robust control algorithms are suggested. As a further improvement of control law for the slow subsystem, two control algorithms are suggested. The first one focused on the avoidance of velocity signal measurement which is useful to eliminate the need of velocity sensors and the second controller aims at avoiding the complex regressor in the control law. Stability analysis and simulation results are also presented.